The long term goal of this research is the development of statistical methods that will allow the estimation of the levels and patterns of migration in natural populations from gene frequency data. The methods developed will be useful for interpreting data on the spatial distribution of genes that can be distinguished by electrophoresis and on data obtained by directly sequencing DNA. This research will be useful for understanding the history and current patterns of migration in natural populations and the methods developed will be useful for understanding the genetic history of human populations It will also be useful for the management of populations including populations of endangered species because it will provide a tool for delimiting the boundaries of independent populations. Furthermore, this research will assist in making predictions about the rate and extent of spread of genetically modified organisms after their intentional or accidental release. The research to be done will be in four general areas. (1) Methods will be developed for estimating the average number of migrants that are exchanged between different populations of a species and for determining whether a species is subject to frequent disturbances. (2) Methods will be developed for inferring the pattern of migration among populations. (3) Methods will be developed for interpreting differences in DNA sequences to allow the tracing of the history of new mutations in a population. (4) Models of the evolutionary dynamics of multigene families will be developed for single populations and for geographically structured populations.